The minority, among whom were prominent Ca" "pals Rauscher and Schwarzenberg, Hefele, bishop of Rotterdam (the historian of the councils) Cardinal Mathieu, Mgr Dupanloup, Mgr Maret, &c., &c., did not pretend to deny the papal infallibility; they pleaded the inopportuneness of the definition and brought forward difficulties mainly of an historical order, in particular the famous condemn ion of Pope Honorius by the 6th ecumenical council of Const: ntinople in 680.
In the notation of the calculus the relations become - dH/dp (0 const) = odv /do (p const) (4) dH/dv (0 const) =odp/do (v const) The negative sign is prefixed to dH/dp because absorption of heat +dH corresponds to diminution of pressure - dp. The utility of these relations results from the circumstance that the pressure and expansion co efficients are familiar and easily measured, whereas the latent heat of expansion is difficult to determine.
The change of energy at constant volume is simply sdo, the change at constant temperature is (odp/de - p)dv, which may be written dE/de (v const) =s, dE/dv (0 const) =odp/do - p .
We thus obtain the relation ds/dv(o const) =od 2 p/d0 2 (v const),.
Observing that F is a function of the co-ordinates expressing the state of the substance, we obtain for the variation of S with pressure at constant temperature, dS/dp (0 const) '=' 2 F/dedp =-0d 2 v/d0 2 (p const) (12) If the heat supplied to a substance which is expanding reversibly and doing external work, pdv, is equal to the external work done, the intrinsic energy, E, remains constant.
The values of the partial differential coefficients in terms of n and c are as follows: - Substituting these values in equations already given, we find, from (6) S - s =R(I +nc/V)2 (24) „ (9) dE/dv (o const) =ncp/V .
F" =S 0 0 - (n+1)cp+bp+B„ dG"/dO (p const) =0" = dJ"/dB (v const)..
(39) dG"/dp (D const) =v, dJ"/dv (0 const) = p. (40) And all the properties of the substance may be expressed in terms of G or J and their partial differential coefficients.
In Vorpommern and Rugen, and thus in the towns of Greifswald, Stralsund and Bergen, among others, the old civic const.itution~ remain unchanged.
Thus, we have 1/2A(2+sin2 0 ~) + 1/2Cn2 + Mgh cos 0 const., (5)
Ofw= const., J
In monochromatic light, then, the interference pattern is characterized by three systems of curves: the curves of constant retardation p = const.; the lines of like polarization = const.; the curves of constant intensity I = const.